[Connection Manager] Properly start/stop Rust thread

We should start it once everything else has started, and
stop it before everything else stops. We can simply kill the
runtime when a Stop arrives - since all futures are meant to
be cancellation safe, this won't leave us in a bad state.

Test: AdapterServiceTest
Bug: 272572974
Change-Id: Ib76070887a43adec5878ceac3c33a27fba13e2eb